We study the convergence of Stochastic Gradient Descent (SGD) for strongly convex objective functions. We prove for all $t$ a lower bound on the expected convergence rate after the $t$-th SGD iteration; the lower bound is over all possible sequences of diminishing step sizes. It implies that recently proposed sequences of step sizes at ICML 2018 and ICML 2019 are {\em universally} close to optimal in that the expected convergence rate after {\em each} iteration is within a factor $32$ of our lower bound. This factor is independent of dimension $d$. We offer a framework for comparing with lower bounds in state-of-the-art literature and when applied to SGD for strongly convex objective functions our lower bound is a significant factor $775\cdot d$ larger compared to existing work.

In this post, you will discover the top 10 books available right now on Artificial Intelligence. There are quite a few available online in which you may purchase. Artificial Intelligence: A Modern Approach, 3e offers the most comprehensive, up-to-date introduction to the theory and practice of artificial intelligence. Number one in its field, this textbook is ideal for one or two-semester, undergraduate or graduate-level courses in Artificial Intelligence. Dr. Peter Norvig, contributing Artificial Intelligence author and Professor Sebastian Thrun, a Pearson author are offering a free online course at Stanford University on artificial intelligence.

Consider a sample y {0, 1} n generated by two different Bernoulli distributions with parameters π 0 and π 1, and consider the set S {1,..., n} as the set of all indices i such that P (y i) π 1 . Assuming that the components of the vector y i are conditionally independent given θ (S, π 0, π 1), the likelihood function is the product of two Binomial distribution functions, and will attain a global maximum at the set S L(y) {i: 1 i n y i 1} (let's call this set the onset of the vector y), with maximum likelihood estimators given by ˆπ 0 0 and ˆπ 1 1. Now consider a design matrix X R n p and a function f: R p {0, 1} such that ψ(X i) 1 i S, where X i is the i-th row of X. Again, if the function f is not constrained in any way, the problem is the same and the same trivial solution applies, with function f defined only in the set of rows of X. In this extreme case, the solution will usually not generalize well, and also will not provide any interesting interpretation (since f is just an enumeration based on the onset of y). Standard methods for the binary classification problem are concerned with the task of estimating f constraining it in different ways such that this trivial solution (associated with the problem of overfitting) is avoided.

Continual learning aims to learn new tasks without forgetting previously learned ones. We hypothesize that representations learned to solve each task in a sequence have a shared structure while containing some task-specific properties. We show that shared features are significantly less prone to forgetting and propose a novel hybrid continual learning framework that learns a disjoint representation for task-invariant and task-specific features required to solve a sequence of tasks. Our model combines architecture growth to prevent forgetting of task-specific skills and an experience replay approach to preserve shared skills. We demonstrate our hybrid approach is effective in avoiding forgetting and show it is superior to both architecture-based and memory-based approaches on class incrementally learning of a single dataset as well as a sequence of multiple datasets in image classification. Our code is available at https://github.

In this paper, we propose a novel method for transforming data into a low-dimensional space optimized for one-class classification. The proposed method iteratively transforms data into a new subspace optimized for ellipsoidal encapsulation of target class data. We provide both linear and non-linear formulations for the proposed method. The method takes into account the covariance of the data in the subspace; hence, it yields a more generalized solution as compared to Subspace Support Vector Data Description for a hypersphere. We propose different regularization terms expressing the class variance in the projected space. We compare the results with classic and recently proposed one-class classification methods and achieve better results in the majority of cases. The proposed method is also noticed to converge much faster than recently proposed Subspace Support Vector Data Description.

We propose a new application of embedding techniques for problem retrieval in adaptive tutoring. The objective is to retrieve problems whose mathematical concepts are similar. There are two challenges: First, like sentences, problems helpful to tutoring are never exactly the same in terms of the underlying concepts. Instead, good problems mix concepts in innovative ways, while still displaying continuity in their relationships. Second, it is difficult for humans to determine a similarity score that is consistent across a large enough training set. We propose a hierarchical problem embedding algorithm, called Prob2Vec, that consists of abstraction and embedding steps. Prob2Vec achieves 96.88\% accuracy on a problem similarity test, in contrast to 75\% from directly applying state-of-the-art sentence embedding methods. It is interesting that Prob2Vec is able to distinguish very fine-grained differences among problems, an ability humans need time and effort to acquire. In addition, the sub-problem of concept labeling with imbalanced training data set is interesting in its own right. It is a multi-label problem suffering from dimensionality explosion, which we propose ways to ameliorate. We propose the novel negative pre-training algorithm that dramatically reduces false negative and positive ratios for classification, using an imbalanced training data set.

In precision medicine, machine learning techniques have been commonly proposed to aid physicians in early screening of chronic diseases. Many of these diseases become more difficult to treat as they progress, so accurate early screening is critical to ensure resources are directed towards the most effective treatment plan [Pagan, 2012]. Since the final treatment decision must inevitably be made by a doctor, these screening procedures should be interpretable such that a clinician can explain the decision-making process to patients for informed consent. However, the types of models that achieve the highest level of accuracy given early screening data tend to be extremely complex, meaning that even machine learning experts have difficulties explaining why certain predictions are made, leading many to describe them as "black box" [Breiman, 2001]. In this paper, we bridge this gap by providing a novel approach for explaining black box model predictions which can give high fidelity explanations with lower model complexity. In particular we will focus on early screening of Parkinson's Disease (PD). PD is a complicated neurodegenerative disorder that affects the central nervous system and specifically the motor control of individuals [mjf, 2019]. This disorder is estimated to affect 930,000 individuals in the US by 2020, and is more prevalent in the geriatric population affecting more then 1% of the population over the age of 60 and 5% of the population over age 85 [Findley, 2007, Kowal et al., 2013, Rossi et al., 2018]. These statistics and other recent studies on Parkinson's epidemiology indicate that as the population ages, the prevalence of PD is expected to grow to over 1.2 million by 2030 in the US alone, increasing the total economic burden of the disorder to approximately $26 billion USD [Kowal et al., 2013, Rossi et al., 2018].

Meta-learning leverages related source tasks to learn an initialization that can be quickly fine-tuned to a target task with limited labeled examples. However, many popular meta-learning algorithms, such as model-agnostic meta-learning (MAML), only assume access to the target samples for fine-tuning. In this work, we provide a general framework for meta-learning based on weighting the loss of different source tasks, where the weights are allowed to depend on the target samples. In this general setting, we provide upper bounds on the distance of the weighted empirical risk of the source tasks and expected target risk in terms of an integral probability metric (IPM) and Rademacher complexity, which apply to a number of meta-learning settings including MAML and a weighted MAML variant. We then develop a learning algorithm based on minimizing the error bound with respect to an empirical IPM, including a weighted MAML algorithm, $\alpha$-MAML. Finally, we demonstrate empirically on several regression problems that our weighted meta-learning algorithm is able to find better initializations than uniformly-weighted meta-learning algorithms, such as MAML.

This study presents early phase detection of Coronavirus (COVID-19), which is named by World Health Organization (WHO), by machine learning methods. The detection process was implemented on abdominal Computed Tomography (CT) images. The expert radiologists detected from CT images that COVID-19 shows different behaviours from other viral pneumonia. Therefore, the clinical experts specify that COV\.ID-19 virus needs to be diagnosed in early phase. For detection of the COVID-19, four different datasets were formed by taking patches sized as 16x16, 32x32, 48x48, 64x64 from 150 CT images. The feature extraction process was applied to patches to increase the classification performance. Grey Level Co-occurrence Matrix (GLCM), Local Directional Pattern (LDP), Grey Level Run Length Matrix (GLRLM), Grey-Level Size Zone Matrix (GLSZM), and Discrete Wavelet Transform (DWT) algorithms were used as feature extraction methods. Support Vector Machines (SVM) classified the extracted features. 2-fold, 5-fold and 10-fold cross-validations were implemented during the classification process. Sensitivity, specificity, accuracy, precision, and F-score metrics were used to evaluate the classification performance. The best classification accuracy was obtained as 99.68% with 10-fold cross-validation and GLSZM feature extraction method.

Bayesian experimental design (BED) is a framework that uses statistical models and decision making under uncertainty to optimise the cost and performance of a scientific experiment. Sequential BED, as opposed to static BED, considers the scenario where we can sequentially update our beliefs about the model parameters through data gathered in the experiment. A class of models of particular interest for the natural and medical sciences are implicit models, where the data generating distribution is intractable, but sampling from it is possible. Even though there has been a lot of work on static BED for implicit models in the past few years, the notoriously difficult problem of sequential BED for implicit models has barely been touched upon. We address this gap in the literature by devising a novel sequential design framework for parameter estimation that uses the Mutual Information (MI) between model parameters and simulated data as a utility function to find optimal experimental designs, which has not been done before for implicit models. Our approach uses likelihood-free inference by ratio estimation to simultaneously estimate posterior distributions and the MI. During the sequential BED procedure we utilise Bayesian optimisation to help us optimise the MI utility. We find that our framework is efficient for the various implicit models tested, yielding accurate parameter estimates after only a few iterations.